SARS检疫隔离控制问题研究II.docx

SARS检疫隔离限制问题探讨IISARS检疫隔离限制问题探讨II刘新金1,邹云21江南高校纺织服装学院，无锡2141222南京理工高校自动化学院，南京210091摘要:在缺乏有效药物和疫苗的状况下，检疫隔离限制是阻挡疾病传播的有效途径。针对此，本文以SARS疾病为例，以检疫隔离限制下SARSSEQIJR多区域传播模型的无病平衡点的稳定性条件为基础，也即防止疾病爆发的条件，详细探讨了区域之间的人口流淌对疾病防控的影响。当描述区域间人口流淌性的耦合矩阵C满意两种特别结构：星型连接与全连接型连接时，对相应的多区域传播模型的无病平衡点的稳定性与检疫隔离限制进行了详细分析°关键词：稳定性：多区域SARSSEQIJR传播模型：人口流淌；检疫隔离限制中图分类号：TP13ThequarantineandisolationcontrolforSARSepidemicsII1.IUXin-Jinl,ZOUYun21SchoolofTextileandClothing,JiangnanUniversity,Wuxi,2141222SchoolofAutomation,NanjingUniversityofScienceandTechnology,Nanjing,210094Abstract:Intheabsenceofvalidmedicinesorvaccine,quarantineandisolationstrategiesarethemostimportantandeffectivemeasuresagainsttheepidemicssuchasSRS(SevereAcuteRespiratorySyndrome).Inthispaper,thestabi1ityanalysisofthedisease-freeequilibriumfortheMulti-areaSEQIJRSRSpropagationmodelwiththequarantineandisolationcontrolwereinvestigated.Theinfluenceoftheinter-areapopulationflowtoSRScontrolweremainlyaddressed.WhenthecouplingmatrixCdescribingtheinter-areapopulationflowhastwospecialstructuresofouter:star-shapedcoupledstructureandgloballycoupledstructure,thestabilityproblemswerestudiedindetails.Keywords:StabiIization;Multi-areaSEQIJRSARSpropagationmodel;Populationflow;Quarantineandisolationcontrol基金项目：NationalNaturalScienceFoundationofP.R.China(60874007),ResearchFundfortheDoctoralProgramofHigherEducation(200802550024)作者简介：Correspondenceauthor：1.IUXin-Jin(1984-),male.1.ecturer,majorresearchdirection：complexdynamicnetworksystems.ZOUYun(1962-),male,professor,majorresearchdirection：singularsystems,multidimensionalsystemandtransientstabi1ityofpowersystems.-1-ingdiscussion.Therefore,n1,n1,0,whenn=2,usingtheresultin1.emma1,themode1(5)isstableifandonIyifA2,A2+ln1O,2ln1Oarestablesimultaneously,i.e.,()()ROS=+1(6)DlD1D2Cs=lCs=l100.0100.0A2=0000B=011000,Ki=0ui0000+ln1E+ln1klWhenAS=InA2+lCstar0isunstable,controllerKitostabilizesystem(5)shouldbedesigned.Firstly,thesamecontrolstrategies:quarantinestrategyuandisolationstrategyvineachareacanbeconsidered,i.e.ul=u2=un=u,vl=v2=vn=v.Withthissimple-1+ln1E+ln1kl21AO0A2A2÷BKl222(n2)l0l0l00A2+BK211Q1D4J2D21v21munityanditshospitalJ.ProceedingsoftheRoyalSocietyof1.ondon-B,2003,270(1528):19791989.13N.Masuda,N.Konno,K.ihara.Transmissionofsevereacuterespiratorysyndromeindynamicalsmal1-worldnetworksJ.PhysicalReviewE,2004,69(3):031917.14G.W.Swan.ApplicationsofOptimalControltheoryinBiomcdicineM.NewYork:MarcelDekker,1984.15D.Kirschner,S.1.enhart,S.Serbin.OptimalcontrolofthechemotherapyofHIVJ.Jour-nalofMathematicalBiology,1997,35:775792.16M.ntonio,1.Caetano,T.Yoneyama.Optimalandsub-optimalcontrolindengueepi-demiesJ.OptimalControl-ApplicationsandMethods,2001,22:6373.17P.Ogren1C.F.Martin.MartinVaccinationstrategiesforepidemicsinhighlymobilepop-ulationsj.pp1iedMathematicsandComputation,2002,127:261276.18X.F.Yan,Y.Zou,J.1.1.i.OptimalquarantineandisolationstrategicsinepidemicscontrolJJ.WorldJournalofModel1ingandSimulation,2007,3(3):202211.19X.F.Yan,Y.Zou.Optimalandsub-optimalquarantineandisolationcontrolinSARSepidemicsj.MathematicalandComputerModel1.ing,2008,47:235245.20X.F.Yan.IsolationTreatmentStrategiesforEmergencyControlD.Nanjing:NanjingUniversityofScienceandTechnology,2007.21X.J.1.iu,Y.Zou.StabilityAnalysisforaspecialclassofDynamicalNetworksJ.Inter-nationalJournalofSystemsScience,DOI:-12-10.1080/00207721.2011.563871,2010.